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    The 3–8-day filtered 850-hPa wind field (vector) and negative OLR anomalies (shaded) on (a) 27 Jun, (b) 29 Jun, (c) 1 Jul, (d) 3 Jul, (e) 5 Jul, and (f) 7 Jul 2002. Shaded areas indicate OLR anomalies of −15, −30, and −45 W m−2. The typhoon symbols denote the locations of cyclogenesis. The letters A and C stand for anticyclonic and cyclonic circulations, respectively. The line segment in Fig. 1a denotes the cross section used in Fig. 2.

  • View in gallery

    The Hovmöller diagram of meridional wind along the northwest–southeast orientation of the wave train in Fig. 1 (m s−1). The abscissa represents longitude and latitude along the cross section while the ordinate corresponds to the date. The arrows denote the energy propagation.

  • View in gallery

    The (top) spatial and (bottom) temporal distribution of specified heating source at σ = 0.5 in the experiments. The x and y axes in the bottom panel denote the integration day and heating rate (K day−1), respectively.

  • View in gallery

    The time evolution of anomalous wind vectors (scale arrow at upper-right corner of each panel) and normalized meridional wind (contour interval of 0.2 m s−1) for the (left) EN and (right) LN runs at days 6, 8, 10, and 12. The wind vectors with wind speed less than 0.01 m s−1 are masked.

  • View in gallery

    The time evolution of meridional wind averaged over 5°S–5°N for the (a) EN and (b) LN runs (m s−1). The abscissa represents longitude and the ordinate corresponds to the integration day. The arrows denote the energy propagation.

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A New Perspective on the Excitation of Low-Tropospheric Mixed Rossby–Gravity Waves in Association with Energy Dispersion

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  • 1 Center for Monsoon System Research, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China
  • | 2 Guy Carpenter Asia-Pacific Climate Impact Centre, School of Energy and Environment, City University of Hong Kong, Hong Kong, China
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Abstract

This study investigates the synoptic-scale equatorial response to Rossby wave energy dispersion associated with off-equatorial wave activity sources and proposes a new mechanism for triggering low-level mixed Rossby–gravity (MRG) waves. A case study based on observations in boreal summer 2002 reveals that a vortex related to tropical cyclogenesis generated a coherent wave train through southeastward energy dispersion. The southeastward-propagating energy packet gave rise to the equatorial atmospheric response with a temporal scale similar to the wave train and with a structure consistent with the equatorially trapped MRG wave. A baroclinic multilevel anomaly model is employed to verify the excitation of MRG associated with the energy dispersion originating outside of the equatorial region and to explore the discrepancy in the equatorial responses under the different background flows corresponding to El Niño and La Niña. The results show that the prevalence of the low-level westerly flow, the associated zonal wind convergence, and the easterly vertical wind shear can be more favorable for the enhancement of southeastward-propagating energy dispersion and equatorial MRG response in the low troposphere during El Niño than those during La Niña. In addition, the strength of the mean flow can strongly affect the extent of equatorial wave response and modulate its phase and group velocity due to the Doppler shift effect.

Corresponding author address: Dr. Guanghua Chen, Center for Monsoon System Research, Institute of Atmospheric Physics, Chinese Academy of Sciences, P.O. Box 2718, Beijing 100190, China. E-mail: cgh@mail.iap.ac.cn

Abstract

This study investigates the synoptic-scale equatorial response to Rossby wave energy dispersion associated with off-equatorial wave activity sources and proposes a new mechanism for triggering low-level mixed Rossby–gravity (MRG) waves. A case study based on observations in boreal summer 2002 reveals that a vortex related to tropical cyclogenesis generated a coherent wave train through southeastward energy dispersion. The southeastward-propagating energy packet gave rise to the equatorial atmospheric response with a temporal scale similar to the wave train and with a structure consistent with the equatorially trapped MRG wave. A baroclinic multilevel anomaly model is employed to verify the excitation of MRG associated with the energy dispersion originating outside of the equatorial region and to explore the discrepancy in the equatorial responses under the different background flows corresponding to El Niño and La Niña. The results show that the prevalence of the low-level westerly flow, the associated zonal wind convergence, and the easterly vertical wind shear can be more favorable for the enhancement of southeastward-propagating energy dispersion and equatorial MRG response in the low troposphere during El Niño than those during La Niña. In addition, the strength of the mean flow can strongly affect the extent of equatorial wave response and modulate its phase and group velocity due to the Doppler shift effect.

Corresponding author address: Dr. Guanghua Chen, Center for Monsoon System Research, Institute of Atmospheric Physics, Chinese Academy of Sciences, P.O. Box 2718, Beijing 100190, China. E-mail: cgh@mail.iap.ac.cn

1. Introduction

Mixed Rossby–gravity (MRG) waves, one of the theoretical solutions to the shallow-water equations, were documented originally in the pioneering work by Matsuno (1966). Since then, the existence of MRG waves has been verified by observations in the upper troposphere and stratosphere (e.g., Yanai and Maruyama 1966; Zangvil and Yanai 1980). The MRG waves are characterized by symmetrical meridional winds and antisymmetric zonal winds about the equator and exhibit a loosely coupled structure between circulation and convection with a phase lag of approximately one-quarter of a wavelength.

The mechanism that triggers the MRG waves in the troposphere is still under debate. Hayashi (1970) proposed a so-called wave-conditional instability of the second kind (wave-CISK). This linear wave-CISK mechanism involves a strong coupling between waves and moist convection in which the interaction between equatorial wave dynamics and cumulus convection can produce unstable modes whose structures resemble those of the MRG waves. Another alternative way is the lateral forcing theory of Mak (1969), who examined the response of tropical atmosphere to the forcing at lateral boundaries (30°N and 30°S) and found large responses with wavenumbers and frequencies corresponding to the observed MRG wave and gravest Rossby mode. This theory was later refined by numerous studies (e.g., Lamb 1973; Zhang 1993). Magaña and Yanai (1995) gave an example of a wave train propagating from the Southern Hemisphere into the tropics through the region where equatorial westerlies form, exciting the MRG waves near the western coast of South America. Recently, based on the nonlinear shallow water equation on the equatorial β plane, Raupp and Silva Dias (2005) revealed that MRG waves can be excited by nonlinear interactions among equatorial waves. In addition, through a case study of tropical cyclogenesis in 2004, Zhou and Wang (2007) found that an upper tropospheric MRG gyre propagated progressively downward and westward. When the gyre approached the date line, the MRG circulation rapidly developed in the lower troposphere, implying that the formation of the low-level MRG wave can be related to its upper-level counterpart.

Many previous studies have revealed that a new tropical cyclogenesis in a synoptic wave train may be closely related to MRG wave transition and Rossby wave energy dispersion (RWED) in the tail of a preexisting tropical cyclone (TC). Dickinson and Molinari (2002) found that the tropical cyclogenesis in summer 1987 is attributable to the transformation from MRG waves to tropical depression (TD)-type disturbances. Chen and Huang (2009) also examined the interannual variation of MRG waves and its influence on tropical cyclogenesis over the western North Pacific (WNP). While a TC moves northwestward, it emits Rossby wave energy southeastward due to the β effect, forming a wave train with alternating anticyclonic and cyclonic vorticity perturbation (e.g., Chan and Williams 1987; Li et al. 2006; Ge et al. 2008). Based on numerical and observational results, Holland (1995) and Li and Fu (2006) indicated that the wave train in association with the southeastward energy propagation can induce a new TC in the wake of a preexisting TC. Given that a TC can form and develop at relatively low latitudes so that the RWED may penetrate into the equatorial region, intriguing questions naturally arise: Is there the equatorial response of MRG wave to the southeastward-propagating energy dispersion? How are the equatorial responses modulated by the different environmental backgrounds? These questions are explored in the present study to advance the understanding of the equatorial response to wave activity off the equator and give an insight into the mechanism responsible for the excitation of equatorial waves.

The paper is organized as follows. In section 2, a case in 2002 in which a vortex produced energy dispersion and then initialized an equatorial MRG response is illustrated. Numerical experiments in which the wave trains are induced by a specified heating impulse are conducted to substantiate the hypothesis of MRG excitation and examine the distinct behaviors of energy dispersion under the different background states in section 3. Conclusions and a discussion are given in section 4.

2. A case study

A case in the summer of 2002 is presented to provide direct observational evidence over the WNP. Figure 1 shows the evolution of the 3–8-day filtered National Centers for Environmental Prediction (NCEP)–National Center of Atmosphere Research (NCAR) reanalysis data and outgoing longwave radiation (OLR) data. On 27 June, a northeast–southwest-tilted cyclonic circulation center (denoted C1) was observed at 6°N, 144°E. At this time, the wave train pattern and equatorial response are hardly discernible. Two days later, the C1 circulation as well as the tightly coupled convection moved northwestward and experienced a contraction in scale. A wavelike pattern can be identified on that day. Meanwhile, Typhoons Rammasum and Chataan formed in the cyclonic regions of the wave train. During the subsequent several days, the low-level atmosphere near the equator started to exhibit wavelike characters with eastward expansion along the equator. In particular, the maximum meridional wind occurred at the equator but without closed circulations. On 5 July, the equatorial atmospheric response was enhanced, leading to the closed cyclonic and anticyclonic circulation centers. The circulations of C3 and A3 were centered on and symmetric about the equator and the convection commenced to decouple with the cyclonic center. Eventually, on 7 July, the cyclonic system (C3) moved away from the equator and intensified, which was accompanied by the formation of the third typhoon, Typhoon Halong. Moreover, the equatorial wave train became more evident and a new cyclonic center (C4) straddling the equator was detected to the east of the A3 anticyclonic circulation region, implying that the energy packet had dispersed to the east of the date line. The active convection had about one-quarter phase difference from the cyclonic center, consistent with the observed MRG structure (e.g., Kiladis et al. 2009) although the horizontal scale was smaller than that over other basins, which is primarily due to the presence of strong zonal wind convergence over the tropical western Pacific. To validate the southeastward energy dispersion, the evolution of meridional wind along the northwest–southeast orientation of the wave train is depicted in Fig. 2. The northwestward phase displacement and southeastward energy dispersion can be detected. The southeastward group velocity of Rossby wave can be approximately estimated at 2.1 m s−1, corresponding to the eastward component of 1.7 m s−1 and the southward component of 1.1 m s−1, which are comparable to the observed in the previous study (Tam and Li 2006).

Fig. 1.
Fig. 1.

The 3–8-day filtered 850-hPa wind field (vector) and negative OLR anomalies (shaded) on (a) 27 Jun, (b) 29 Jun, (c) 1 Jul, (d) 3 Jul, (e) 5 Jul, and (f) 7 Jul 2002. Shaded areas indicate OLR anomalies of −15, −30, and −45 W m−2. The typhoon symbols denote the locations of cyclogenesis. The letters A and C stand for anticyclonic and cyclonic circulations, respectively. The line segment in Fig. 1a denotes the cross section used in Fig. 2.

Citation: Journal of the Atmospheric Sciences 69, 4; 10.1175/JAS-D-11-0331.1

Fig. 2.
Fig. 2.

The Hovmöller diagram of meridional wind along the northwest–southeast orientation of the wave train in Fig. 1 (m s−1). The abscissa represents longitude and latitude along the cross section while the ordinate corresponds to the date. The arrows denote the energy propagation.

Citation: Journal of the Atmospheric Sciences 69, 4; 10.1175/JAS-D-11-0331.1

The above observational fact illustrates a sequence of evolution of an off-equatorial wave train associated with a preexisting vortex and the appearance of MRG wave at the equator. A noticeable characteristic of the wave train is that its meridional scale is larger than its zonal scale, which is essential for the southeastward energy propagation (Li et al. 2003). Based on the Rossby wave dispersion relationship, wave energy propagates eastward when the meridional wavelength exceeds the zonal wavelength, and an opposite sign of the zonal and meridional wavenumber (corresponding to a northwestward phase speed) leads to a southward energy propagation component. In addition, the off-equatorial disturbances and equatorial MRG waves have an overlapping wavenumber–frequency regime (e.g., Wheeler et al. 2000). These imply that the excitation of equatorial MRG wave is closely related to the RWED associated with the off-equatorial wave train. To verify this hypothesis, a baroclinic model is employed to reproduce this evolution and distinguish the equatorial responses to the energy dispersion under the different background flows.

3. Numerical results

The global spectral anomaly model, which is constructed based on the dynamic core of the Geophysical Fluid Dynamics Laboratory AGCM (Held and Suarez 1994), is used in this study. The model has a horizontal resolution of T42 and an equally distributed five-level sigma coordinate; it consists of primitive equations linearized by a realistic three-dimensional basic state but retains full nonlinearity in the second-order perturbation terms of the prediction equations. Using this model, Wang et al. (2003) studied an equatorially asymmetric atmospheric response to a symmetric forcing, and Li (2006) examined the origin of the synoptic-scale wave in boreal summer over the WNP.

Inspired by Sobel and Horinouchi (2000), Rossby wave energy dispersion is generated by introducing an impulse-like heating off the equator. Its spatial and temporal distributions are specified as follows:
eq1
where λ, φ, and T denote longitude, latitude, and integration time: λ0, φ0, and T0 are set to correspond to 157.5°E, 12.6°N, and the fifth day of integration, and Δλ, Δφ, and ΔT are equivalent to 14.1°, 8.3°, and 0.5 day. Consequently, the heating source with an elliptic spatial distribution and a Gauss-shaped temporal distribution is specified (shown in Fig. 3). The maximum heating rate is prescribed to 2 K day−1 and then is multiplied by 0.2, 0.7, 1.0, 0.5, and 0.1 at σ = 0.1, 0.3, 0.5, 0.7, and 0.9, respectively, to represent the vertical variation of heating.
Fig. 3.
Fig. 3.

The (top) spatial and (bottom) temporal distribution of specified heating source at σ = 0.5 in the experiments. The x and y axes in the bottom panel denote the integration day and heating rate (K day−1), respectively.

Citation: Journal of the Atmospheric Sciences 69, 4; 10.1175/JAS-D-11-0331.1

To compare the equatorial atmospheric responses to RWED under the different environmental fields, the 3D July–September mean fields in El Niño (EN; 1965, 1972, 1982, 1987, 1997, 2002) and La Niña (LN; 1964, 1973, 1975, 1988, 1998, 1999) are specified. The remarkable differences between the two kinds of extreme cases are that the low-tropospheric westerly flows penetrate eastward and give rise to enhanced zonal wind convergence and easterly vertical shear in the eastern part of WNP during EN. In contrast, the westerly flows retreat westward over the Philippines and the easterly flows dominate to the east of 130°E during LN.

Because the meridional wind at the equator is the best indicative quantity that characterizes the MRG activity, Fig. 4 demonstrates the time evolutions of meridional winds and wind fields in response to the specified heating source peaking at the fifth day during EN and LN. At the early stage, the two experiments show similar circulation signatures (i.e., the cyclonic circulations are located north of 10°N). However, the wave responses triggered by the heating source exert gradually their influences in the equatorial region. At day 8, marked differences can be found. During EN, the energy dispersion generates the maximum equatorial meridional winds southeast of the heating source, leading to a cyclonic circulation symmetric about the equator at 170°E. The equatorial response is consistent with the MRG wave structure and continues to expand eastward while the MRG phase propagates westward. At day 10, the MRG response shifts eastward to the date line. Although the wind speeds decay gradually because of the friction damping, the equatorial response east of the date line can still be detected at day 12. In sharp contrast, during LN the low-tropospheric equatorial response is confined to the west of 160°E; moreover, the equatorial wave packet migrates westward, indicating a westward energy propagation. Additionally, different from the results in EN, the experiment cannot produce evident MRG wave structures in LN.

Fig. 4.
Fig. 4.

The time evolution of anomalous wind vectors (scale arrow at upper-right corner of each panel) and normalized meridional wind (contour interval of 0.2 m s−1) for the (left) EN and (right) LN runs at days 6, 8, 10, and 12. The wind vectors with wind speed less than 0.01 m s−1 are masked.

Citation: Journal of the Atmospheric Sciences 69, 4; 10.1175/JAS-D-11-0331.1

To verify the above results, the evolution of meridional wind averaged over 5°S–5°N is depicted in Fig. 5. The equatorial response during EN is characterized by an eastward-propagating energy packet with a group velocity of about 3.2 m s−1 and a slow westward-shifting phase speed of 6.3 m s−1. In contrast, westward-propagating energy dispersion and relatively fast phase migration are observed during LN. Another noticeable feature is that the coherent energy propagation can persist for a long period during EN compared to a rapid decay during LN.

Fig. 5.
Fig. 5.

The time evolution of meridional wind averaged over 5°S–5°N for the (a) EN and (b) LN runs (m s−1). The abscissa represents longitude and the ordinate corresponds to the integration day. The arrows denote the energy propagation.

Citation: Journal of the Atmospheric Sciences 69, 4; 10.1175/JAS-D-11-0331.1

The aforementioned distinctions in the equatorial wave responses can be attributed to the modulation of background flows from the purely dynamic point of view. If the longitudinally asymmetric basic state includes a “duct” in which the zonal winds are westerly, waves with a zonal scale less than that of the westerly duct may propagate from the extratropical region to the equatorial zone and even to the other hemisphere (e.g., Webster and Holton 1982; Tomas and Webster 1994). Besides, the mean flows can modulate the Rossby wave group velocity through a “Doppler shift effect.” As the energy dispersion progresses southeastward, the low-level mean westerly (easterly) flow can enhance (reduce) the total group velocity and thus give rise to the equatorial response at a longitude that is farther (less far) east. In addition, the westerly background flows are favorable for triggering strong convectively coupled waves, leading to a slower westward-shifting phase speed during EN than during LN. On the other hand, in the presence of vertical wind shear, a barotropic mode may be excited because of the baroclinic forcing. The baroclinic and barotropic modes are coupled in such a way that the two modes are nearly in phase in the westerly shear, while they are out of phase in the easterly shear. Therefore, an easterly (westerly) shear leads to the amplification of Rossby waves in the lower (upper) level (Wang and Xie 1996). In addition, the wave train tends to experience an energy accumulation process in a confluent mean zonal flow (Kuo et al. 2001) that is favorable for the energy supply to the equatorial response. Hence, compared to the situation during LN, the wave train is embedded in the region of the enhanced westerly flow and its associated zonal flow convergence and easterly vertical wind shear during EN. These favorable dynamic environmental fields in collaboration with the wave train characteristics can help the equatorward and eastward propagation of energy dispersion in the low troposphere and then strengthen the energy accumulation in the equatorial region. The equatorial response to the energy dispersion yields eventually the equatorially trapped MRG-like structure with a wavenumber–frequency domain similar to the synoptic wave train off the equator.

4. Summary and discussion

Different from the wave–convection feedback, nonlinear interactions among equatorial waves, and lateral forcing in previous studies, this study explores a possible mechanism for the excitation of low-tropospheric equatorial MRG waves based on observational analysis and numerical experiments. A clear connection between the generation of a wave train off the equator associated with the energy dispersion in the wake of a preexisting vortex and the subsequent initialization of equatorial MRG wave is illustrated in a case study for the boreal summer 2002. The results of the global baroclinic anomaly model indicate that the dynamic environmental fields during EN are more likely to produce a southeastward propagation of energy dispersion originating outside of the equatorial region and a coherent equatorial response than during LN. To a large extent, the differences can be attributed to the distinct dynamic effects associated with the flow patterns. In contrast to the situation during LN, the presence of low-tropospheric westerly flow during EN can provide a westerly duct and a Doppler shift effect, favorable for the southeastward propagation of energy dispersion. Moreover, the zonal wind confluence and easterly vertical wind shear help energy accumulation in the equatorial region and confine the wave amplification to the low troposphere, leading to an enhancement and eastward expansion of the equatorial MRG wave response.

Many previous studies depicted a commonly observed sequence of the equatorial MRG wave and off-equatorial wave train. The westward-propagating MRG waves, when penetrating into the monsoon region over the WNP, experience a scale contraction and then deviate from the equator and evolve into tropical depression (TD)-type disturbances. This transition can play a crucial role in providing seedlings for tropical cyclogenesis (e.g., Liebmann and Hendon 1990; Takayabu and Nitta 1993; Frank and Roundy 2006). This study points out a possible reversible process, namely that tropical cyclogenesis can excite the equatorial MRG wave through southeastward energy dispersion. Therefore, a tropical cyclogenesis in association with either MRG wave transition or energy dispersion in the wake of a preexisting TC may be subject to their joint influence and followed by their cycling process, leading to more successive cyclogenesis. Finally, it should be pointed out that in the current multilevel model, the thermodynamic effects such as circulation–convection feedback are ignored. In addition, the sensitivity of the equatorial response to the formation location and strength of synoptic wave train off the equator needs to be further investigated in a 3D model with more realistic moist physical processes.

Acknowledgments

We thank Dr. Renguang Wu for helpful modification for our manuscript. C.-Y. Tam is grateful to Tim Li and Xianan Jiang for discussions in the initial stage of this project at the University of Hawaii. This study was supported by the Special Scientific Research project for Public Welfare (Grant GYHY201006021), the National Natural Science Foundation of China (Grants 40905024 and 40921160379), and the City University of Hong Kong (Grant 7008076).

REFERENCES

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    • Search Google Scholar
    • Export Citation
  • Chen, G., , and R. Huang, 2009: Interannual variation of the mixed Rossby–gravity waves and their impact on tropical cyclogenesis over the western North Pacific. J. Climate, 22, 535549.

    • Search Google Scholar
    • Export Citation
  • Dickinson, M., , and J. Molinari, 2002: Mixed Rossby–gravity waves and western Pacific tropical cyclogenesis. Part I: Synoptic evolution. J. Atmos. Sci., 59, 21832196.

    • Search Google Scholar
    • Export Citation
  • Frank, W. M., , and P. E. Roundy, 2006: The role of tropical waves in tropical cyclogenesis. Mon. Wea. Rev., 134, 23972417.

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    • Search Google Scholar
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    • Search Google Scholar
    • Export Citation
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